Crystalline Field and Spin Polarization Effects on Electron Densities and Magnetic Form Factors

Abstract

The combined effects of spin (or exchange) polarization and an external crystalline field on charge densities, x-ray and magnetic form factors, and hyperfine parameters are investigated following the analytic Hartree-Fock self-consistent field approach. The crystalline field was represented by a crude cubic field arising from an octahedral array of point charges surrounding the central ion---in this case ${\mathrm{Ni}}^{+2}$. In the strong field approximation the atomic $3d$ electrons are "split" by the crystalline field and the spinpolarization effect, resulting in a description of these electrons by a set of three distinct orbitals (each having different radial distributions and called ${t}_{2g}\ensuremath{\uparrow}$, ${t}_{2g}\ensuremath{\downarrow}$ and ${e}_{g}\ensuremath{\uparrow}$). The ion's spin density leads to a Fermi contact hyperfine term in better agreement with experiment than the value reported in an earlier spin polarized calculation for the free ${\mathrm{Ni}}^{+2}$ ion and a magnetic form factor whose Fourier transform resembles none of the individual $3d$ charge distributions.